Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1 Scheduling: CrossChek Golf Club Manufacturing • CrossChek sporting goods is considering a process for development of a new golf club • Processing times, as well as constraints over when each step in the process can start are given in the next slide • CrossChek would like to have a few questions about the process answered: • How long does the process take (i.e. the least amount of time)? • What are the scheduled start and end times for each activity? • Which activities are critical? That is, which activities must be completed on time to keep the project on schedule? • For how long can non-critical activities be delayed? 2 Scheduling Golf Club Production Activity Description Predecessors Time (days) A Planning -- 10 B Club face forging A 8 C Shaft construction A 14 D Club head manufacturing B, C 8 E Gripping C 7 F Assembly D, E 12 G Balancing F 10 3 The Critical Path Method (CPM) • How can we answer these questions: • How long does the process take (i.e. the least amount of time)? • What are the scheduled start and end times for each activity? • Which activities are critical? That is, which activities must be completed on time to keep the project on schedule? • For how long can non-critical activities be delayed? 4 The Critical Path Method (CPM) • For each activity, let: • t: the time it takes to complete • ES: the earliest start time • EF: the earliest finish time • LS: the latest start time • LF: the latest finish time • Create a predecessor graph, called a project graph • One node for each activity: Activity ES EF t LS LF 5 The Critical Path Method (CPM) • “Slack” or “Float” • The amount of time an activity can be delayed without affecting the overall project completion time • Computed by LS – ES or LF – EF • There will always be a path of activities with no float • This path is known as the critical path 6 The Critical Path Method (CPM) • We can now answer these questions: • How long does the process take (i.e. the least amount of time)? • 54 days • What are the scheduled start and end times for each activity? • See ES, EF for each activity • Which activities are critical? That is, which activities must be completed on time to keep the project on schedule? • Planning-Shaft construction-Club head manufacturing-Assembly- Balancing • For how long can non-critical activities be delayed? • Club face forging: 6 days; Gripping: 1 day 7 Project Acceleration • CrossChek management finds that the results of the scheduling analysis are unacceptable, and that the project must be completed within 50 days. Management appreciates that project activity times can only be reduced so much, and that there will be costs associated with these reductions 8 Crashing • Commonly used term for project acceleration • The minimum amount of time in which an activity can be completed (i.e. under maximum acceleration) is known as its crash time • The per-unit cost of accelerating an activity is known as its crash cost 9 Project Acceleration for CrossChek Activity Description Predecessors Time Crash Time Crash Cost (1000’s) A Planning -- 10 8 400 B Club face forging A 8 7 600 C Shaft construction A Club head B, C manufacturing 14 10 300 8 5 100 D E Gripping C 7 3 200 F Assembly D, E 12 9 300 G Balancing F 10 8 500 10 LP for CrossChek Crashing Problem Min 400yA + 600yB + 300yC + 100yD + 200yE + 300yF + 500yG st xA + yA > 10 xB + yB - xA > 8 xC + yC - xA > 14 xD + yD - xB > 8 xD + yD - xC > 8 xE + yE - xC > 7 xF + yF - xD > 12 xF + yF - xE > 12 xG + yG - xF > 10 yA < 2 yB < 1 yC < 4 yD < 3 yE < 4 yF < 3 yG < 2 xG < 50 11 LINDO Solution VARIABLE YA YB YC YD YE YF YG XA XB XC XD XE XF XG VALUE 0.000000 0.000000 0.000000 3.000000 2.000000 1.000000 0.000000 10.000000 24.000000 24.000000 29.000000 29.000000 40.000000 50.000000 REDUCED COST 100.000000 600.000000 0.000000 0.000000 0.000000 0.000000 200.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000